Construction and Visualization of Confidence Sets for Frequentist Distributional Forecasts

References

• Amisano, G., and Giacomini, R. (2007), “Comparing Density Forecasts via Weighted Likelihood Ratio Tests,” Journal of Business and Economic Statistics, 25, 177–190.
   Web of Science ®Google Scholar
• Andersen, T. G., Bollerslev, T, and Diebold, F. X. (2007), “Roughing It Up: Including Jump Components in the Measurement, Modeling and Forecasting of Return Volatility,” The Review of Economics and Statistics, 89, 701–720.
   Web of Science ®Google Scholar
• Andersen, T. G., Bollerslev, T., Diebold, F. X., and Labys, P. (2003), “Modelling and Forecasting Realized Volatility,” Econometrica, 71, 579–625.
   Web of Science ®Google Scholar
• Bengtsson, H. (2015), R.matlab: Read and Write MAT Files and Call MATLAB from Within R. R Package Version 3.2.0, available at http://CRAN.R-project.org/package=R.matlab
   Google Scholar
• Boero, G., Smith, J, and Wallis, K. F. (2011), “Scoring Rules and Survey Density Forecasts,” International Journal of Forecasting, 27, 379–393.
   Web of Science ®Google Scholar
• Bollerslev, T., Kretschmer, U., Pigorsch, C., and Tauchen, G. (2009), “A Discrete-Time Model for Daily S&P500 Returns and Realized Variations: Jumps and Leverage Effects,” Journal of Econometrics, 150, 151–166.
   Web of Science ®Google Scholar
• Brownlees, C. T., and Gallo, G. M. (2006), “Financial Econometric Analysis at Ultra-High Frequency: Data Handling Concerns,” Computational Statistics and Data Analysis, 51, 2232–2245.
   Web of Science ®Google Scholar
• Choi, S., Hall, W. J., and Schick, A. (1996), “Asymptotically Uniformly Most Powerful Tests in Parametric and Semiparametric Models,” The Annals of Statistics, 24, 841–861.
   Web of Science ®Google Scholar
• Corradi, V., and Swanson, N. (2006), “Predictive Density and Conditional Confidence Interval Accuracy Tests,” Journal of Econometrics, 135, 187–228.
   Web of Science ®Google Scholar
• Corsi, F. (2009), “A Simple Approximate Long Memory Model of Realized Volatility,” Journal of Financial Econometrics, 7, 174–196.
   Web of Science ®Google Scholar
• Cox, D. R., and Hinkley, D. V. (1974), Theoretical Statistics, London: Chapman and Hall.
   Google Scholar
• Czado, C., Gneiting, T., and Held, L. (2009), “Predictive Model Assessment for Count Data,” Biometrics, 65, 1254–1261.
   PubMed Web of Science ®Google Scholar
• Dawid, A. P. (1984), “Present Position and Potential Developments: Some Personal Views. Statistical Theory. The Prequential Approach,” Journal of the Royal Statistical Society, Series A, 147, 278–292.
   Google Scholar
• De Gooijer, J. G., and Hyndman, R. (2006), “25 Years of Time Series Forecasting,” International Journal of Forecasting, 22, 443–473.
   Web of Science ®Google Scholar
• Diebold, F. X., Gunther, T. A, and Tay, A. S. (1998), “Evaluating Density Forecasts with Applications to Financial Risk Management,” International Economic Review, 39, 863–883.
   Web of Science ®Google Scholar
• Freeland, R., and McCabe, B. (2004), “Forecasting Discrete Valued Low Count Time Series,” International Journal of Forecasting, 20, 427–434.
   Web of Science ®Google Scholar
• Geweke, J. (2005), Contemporary Bayesian Econometrics and Statistics, New York: Wiley.
   Google Scholar
• Geweke, J., and Amisano, G. (2010), “Comparing and Evaluating Bayesian Predictive Distributions of Asset Returns, Special Issue on Bayesian Forecasting in Economics,” International Journal of Forecasting, 26, 216–230.
   Web of Science ®Google Scholar
• Gneiting, T., Balabdaoui, F., and Raftery, A. (2007), “Probabilistic Forecasts, Calibration and Sharpness,” Journal of the Royal Statistical Society, Series B, 69, 243–268.
   Google Scholar
• Gneiting, T., and Katzfuss, M. (2014), “Probabilistic Forecasting,” Annual Review of Statistics and Its Application, 1, 125–151.
   Web of Science ®Google Scholar
• Gneiting, T., and Raftery, A. E. (2007), “Strictly Proper Scoring Rules, Prediction, and Estimation,” Journal of the American Statistical Association, 102, 359–378.
   Web of Science ®Google Scholar
• Hansen, B. E. (1994), “Autoregressive Conditional Density Estimation”, International Economic Review, 35, 705–730.
   Web of Science ®Google Scholar
• Jensen, M. J., and Maheu, J. M. (2014), “Estimating a Semiparametric Asymmetric Stochastic Volatility Model with a Dirichlet Process Mixture,” Journal of Econometrics, 178, 523–538.
   Web of Science ®Google Scholar
• Le Cam, L., and Yang, G. L. (1990), Asymptotics in Statistics: Some Basic Concepts, New York: Springer.
   Google Scholar
• Maheu, J. M., and McCurdy, T. H. (2011), “Do High-Frequency Measures of Volatility Improve Forecasts of Return Distribution?” Journal of Econometrics, 160, 69–76.
   Web of Science ®Google Scholar
• Maneesoonthorn, W., Martin, G. M., Forbes, C. S., and Grose, S. G. (2012), “Probabilistic Predictions of Volatility and its Risk Premia,” Journal of Econometrics, 171, 217–236.
   Web of Science ®Google Scholar
• McCabe, B., Martin, G. M., and Harris, D. (2011), “Efficient Probabilistic Forecasts for Counts,” Journal of the Royal Statistical Society, Series B, 73, 253–272.
   Google Scholar
• Phillips, P. C. B. (1979), “The Sampling Distribution of Forecasts from a First-Order Autoregression,” Journal of Econometrics, 9, 241–261.
   Google Scholar
• Politis, D. N., Romano, J. P., and Wolf, M. (1999), Subsampling, New York: Springer.
   Google Scholar
• Rodriguez, A., and Ruiz, E. (2009), “Bootstrap Prediction Intervals in State-Space Models,” Journal of Time Series Analysis, 30, 167–178.
   Web of Science ®Google Scholar
• ——— (2012), “Bootstrap Prediction Mean Squared Errors of Unobserved States Based on the Kalman Filter with Estimated Parameters,” Computational Statistics and Data Analysis, 56, 62–74.
   Web of Science ®Google Scholar
• Schweder, T., and Hjort, N. L. (2016), Confidence, Likelihood, Probability: Statistical Inference with Confidence Distributions, New York: Cambridge University Press.
   Google Scholar
• Shao, J. (2003), Mathematical Statistics, New York: Springer-Verlag.
   Google Scholar
• Tay, A. S., and Wallis, K. (2000), “Density Forecasting: A Survey,” Journal of Forecasting, 19, 235–254.
   Web of Science ®Google Scholar
• Wald, A. (1943), “Tests of Statistical Hypotheses Concerning Several Parameters When the Number of Observations is Large,” Transactions of the American Mathematical Society, 54, 426–482.
   Google Scholar
• Wolf, M., and Wunderli, D. (2015), “Bootstrap Joint Prediction Regions,” Journal of Time Series Analysis, 36, 352–376.
   Web of Science ®Google Scholar
• Xie, Y. (2013), “Animation: An R Package for Creating Animations and Demonstrating Statistical Methods,” Journal of Statistical Software, 53, 1–27. Available at http://www.jstatsoft.org/v53/i01/
   Web of Science ®Google Scholar